A294009 - OEIS

%I #4 Oct 21 2017 21:20:58

%S 1,2,7,22,73,240,818,2824,9995,36210,134397,511802,1999360,8023808,

%T 33066865,140066840,609466485,2725084766,12510393090,58957378290,

%U 284932585092,1411369884766,7157365741706,37132616218394,196866561660145,1065754768886044

%N Number of multisets of exactly seven nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%H Alois P. Heinz, <a href="/A294009/b294009.txt">Table of n, a(n) for n = 7..806</a>

%F a(n) = [x^n y^7] Product_{j>=1} 1/(1-y*x^j)^A000085(j).

%p g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:

%p b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,

%p       add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 8)

%p     end:

%p a:= n-> coeff(b(n$2), x, 7):

%p seq(a(n), n=7..40);

%Y Column k=7 of A293808.

%Y Cf. A000085.

%K nonn

%O 7,2

%A _Alois P. Heinz_, Oct 21 2017